Question

Y=tan^-1(π/2-x)+tan^-1x . find dy/dx

Answer 1

Step-by-step explanation:

Y=tan^-1(π/2-x)+tan^-1x . find dy/dxHow do you prove tan−1x+tan−1(1x)=π2 for x>0?

Trigonometry  Proving Identities

2 Answers

sjc

Jan 13, 2017

we first need to know the following relationships between tanθ &cotθ

we have:

cotθ=1tanθ

also

cotθ=tan(π2−θ)

Explanation:

let y=tan−1x⇒x=tany

x=tany⇒1x=1tany=coty

1x=coty=tan(π2−y)

∴π2−y=